Written by **Sagar Rabidas**February 3, 2022

14 min read

C++

Software Developer

A binary search tree in C++ is defined as a data shape that consists of the node-primarily based binary tree where each node consists of at most 2 nodes that are called infant nodes. This tree is also called an ordered or sorted tree. The usage of this idea, you may store numbers in an organized way and a binary tree helps in a quick search, upload, and/or delete operations to be executed on the dataset. Using the idea you possibly can implement dynamic sets and research tables. The shape of the binary tree permits skipping of half of the final tree accordingly leading to higher time complexity with the average being o(log n) for seek, upload, and/or delete operations. This technique is higher than the linear search due to its improved time complexity. In this newsletter, we will examine all of the standards of addition, seek and delete in the first-rate element.

Retrieve the value of root in a Binary Search tree:

root->key

Point to the left of the root in a Binary Search tree:

root->left

Point to the right of the root in a Binary Search tree:

root->right

By now we understand that the Binary Search tree (BST) has a root node and at max 2 child nodes either on to left or right or both. The algorithm in a BST undergoes operations by comparison of values in the root node, and subsequently, it is lesser or more, the navigation in the tree takes place accordingly. In the working of Binary search tree, 3 operations are performed, namely:

**Insert:**In this operation, if the tree is empty, the first value that is inserted is always the root node, now when the next value is inserted, it compares if the value is greater than the root node or not. If greater it gets inserted to the right-hand side and if not, it moves to the left. If there is already a left side existing while inserting, it checks till the last node is hit and subsequently based on it being more or less, gets inserted into the corresponding location of the node.**Search:**This is fairly an easy operation, where the number which needs to be searched is compared against the node values that are present. If the value that needs to be searched is more than the node value, the right side of the tree is searched and vice versa. In this way, we can avoid the other half of the tree which need not be searched as the binary tree is an ordered one. Till the end, if the node is NULL, we return that the value is not found.**Delete:**Finally coming to the delete, which is one of the toughest amongst the three, but here we are to simplify it for you. When we delete, we might have 3 possibilities that we will discuss below one by one:**Case 1:**The leaf node is to be deleted. When the number which needs to be deleted lies in the leaf, which means that there are no other values as a branch, we simply navigate to that location and delete the leaf node.**Case 2:**One leaf node is attached to the root node. Here we navigate to the node which contains one leaf node, delete the node and assign that leaf node as the root node.**Case 3:**The node that desires to be deleted has 2 leaf nodes connected to it. Right here we discover the in-order successor of the node, then replica all of the contents of the in-order successor observed using replacing the deleted node with the so as successor and pasting the contents of the in-order successor on the node which changed the deleted node. The in-order successor is the maximum value on the proper aspect of the tree from the node where the value is deleted from.

With the understanding of the above 3 processes, it will be easier to now look at some examples, to get the practical experience of the theory we just learned.

Here are the following examples mentioned below:

Insert in Binary Search Tree in C++

#include <iostream>

using namespace std;

class nodeBST

{

int key;

nodeBST *lft, *rgt;

public:

nodeBST();

nodeBST(int);

nodeBST* insertFunc(nodeBST*, int);

void traverseInOrder(nodeBST*);

};

nodeBST ::nodeBST()

: key(0)

, lft(NULL)

, rgt(NULL)

{

}

nodeBST ::nodeBST(int value)

{

key = value;

lft = rgt = NULL;

}

nodeBST* nodeBST ::insertFunc(nodeBST* root, int value)

{

if (!root)

{

return new nodeBST(value);

}

if (value > root->key)

{

root->rgt = insertFunc(root->rgt, value);

}

else

{

root->lft = insertFunc(root->lft, value);

}

return root;

}

void nodeBST ::traverseInOrder(nodeBST* root)

{

if (!root) {

return;

}

traverseInOrder(root->lft);

cout << root->key << endl;

traverseInOrder(root->rgt);

}

int main()

{

nodeBST node, *root = NULL;

root = node.insertFunc(root, 0);

node.insertFunc(root, 27);

node.insertFunc(root, 9);

node.insertFunc(root, 19);

node.insertFunc(root, 91);

node.insertFunc(root, 2);

node.insertFunc(root, 7);

cout<<"\nThe sorted binary search tree is "<< endl;

node.traverseInOrder(root);

return 0;

}

Search in Binary Search Tree in C++.

#include <iostream>

using namespace std;

class nodeBST

{

public:

int key;

nodeBST *lft, *rgt;

nodeBST();

nodeBST(int);

nodeBST* insertFunc(nodeBST*, int);

nodeBST* searchFunc(nodeBST*, int);

void traverseInOrder(nodeBST*);

};

nodeBST ::nodeBST()

: key(0)

, lft(NULL)

, rgt(NULL)

{

}

nodeBST ::nodeBST(int value)

{

key = value;

lft = rgt = NULL;

}

nodeBST* nodeBST ::insertFunc(nodeBST* root, int value)

{

if (!root)

{

return new nodeBST(value);

}

if (value > root->key)

{

root->rgt = insertFunc(root->rgt, value);

}

else

{

root->lft = insertFunc(root->lft, value);

}

return root;

}

nodeBST* nodeBST ::searchFunc(nodeBST* root, int key)

{

if (root == NULL || root->key == key)

return root;

if (root->key < key)

return searchFunc(root->rgt, key);

return searchFunc(root->lft, key);

}

void nodeBST ::traverseInOrder(nodeBST* root)

{

if (!root) {

return;

}

traverseInOrder(root->lft);

cout << root->key << endl;

traverseInOrder(root->rgt);

}

int main()

{

nodeBST node, *root = NULL, *searchRoot = NULL;

root = node.insertFunc(root, 0);

node.insertFunc(root, 27);

node.insertFunc(root, 9);

node.insertFunc(root, 19);

node.insertFunc(root, 91);

node.insertFunc(root, 2);

node.insertFunc(root, 7);

cout<<"\nThe sorted binary search tree is "<< endl;

node.traverseInOrder(root);

cout<<"\nSearch for 7 in the BST "<< endl;

searchRoot = node.searchFunc(root, 7);

if(searchRoot == NULL)

{

cout<<"Value Not Found\n";

}

else

{

cout << "Value Found! "<<searchRoot->key<<"\n";

}

cout<<"\nSearch for 2709 in the BST "<< endl;

*searchRoot = NULL;

searchRoot = node.searchFunc(root, 2709);

if(searchRoot == NULL)

{

cout<<"Value Not Found\n";

}

else

{

cout << "Value Found! "<<searchRoot->key<<"\n";

}

return 0;

}

Delete in Binary Search Tree in C++.

#include <bits/stdc++.h>

using namespace std;

struct node {

int key;

struct node *lft, *rgt;

};

struct node* newNode(int item)

{

struct node* temp

= (struct node*)malloc(sizeof(struct node));

temp->key = item;

temp->lft = temp->rgt = NULL;

return temp;

}

void inorder(struct node* root)

{

if (root != NULL) {

inorder(root->lft);

cout << root->key << " ";

inorder(root->rgt);

}

}

struct node* insertFunc(struct node* node, int val)

{

if (!node)

{

return newNode(val);

}

if (val > node->key)

{

node->rgt = insertFunc(node->rgt, val);

}

else

{

node->lft = insertFunc(node->lft, val);

}

return node;

}

struct node* minValueNode(struct node* node)

{

struct node* current = node;

while (current && current->lft != NULL)

current = current->lft;

return current;

}

struct node* deleteFunc(struct node* root, int key)

{

if (root == NULL)

return root;

if (key < root->key)

root->lft = deleteFunc(root->lft, key);

else if (key > root->key)

root->rgt = deleteFunc(root->rgt, key);

else {

if (root->lft==NULL and root->rgt==NULL)

return NULL;

else if (root->lft == NULL) {

struct node* temp = root->rgt;

free(root);

return temp;

}

else if (root->rgt == NULL) {

struct node* temp = root->lft;

free(root);

return temp;

}

struct node* temp = minValueNode(root->rgt);

root->key = temp->key;

root->rgt = deleteFunc(root->rgt, temp->key);

}

return root;

}

int main()

{

struct node* root = NULL;

root = insertFunc(root, 27);

root = insertFunc(root, 9);

root = insertFunc(root, 19);

root = insertFunc(root, 91);

root = insertFunc(root, 2);

root = insertFunc(root, 7);

root = insertFunc(root, 0);

root = insertFunc(root, 1);

cout << "Inorder traversal of the given tree \n";

inorder(root);

cout << "\n<Delete> 1\n";

root = deleteFunc(root, 1);

cout << "Traversing the modified tree \n";

inorder(root);

cout << "\n<Delete> 19\n";

root = deleteFunc(root, 19);

cout << " Traversing the modified tree \n";

inorder(root);

cout << "\n<Insert> 72\n";

root = insertFunc(root, 72);

cout << " Traversing the modified tree \n";

inorder(root);

cout << "\n<Delete> 7\n";

root = deleteFunc(root, 7);

cout << " Traversing the modified tree \n";

inorder(root);

return 0;

}

C

C++

Binary search tree

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